When you're creating an account with an email and password, you have the option to back up your encrypted private key on the Ambire Cloud - we recommend using this option!
The Ambire Cloud is a secure storage which can be used for backing up encrypted private keys. If you opt-in, one of the two private keys which make up an email/password account will be stored encrypted with the password you chose, in the Ambire Cloud. The encryption algorithms used are scrypt for deriving the symmetric key, and AES-128-CTR.
If you opt-out of Ambire Cloud, you must download a JSON file back up from the Security page of your Ambire Wallet. If you clear your browser storage and you don't have a JSON back up, or if you forget your password, you will have to trigger the recovery procedure. The recovery procedure has to be triggered on each blockchain separately and involves a network fee, which depends on the network and a waiting period of 3 days. You will also not be able to login into the same account on a different device without importing the JSON file backup. You would also need the JSON file to sign any transactions.
For more details on how all of this works under the hood, see the Ambire Wallet security model.
You can opt-out at a later stage by just adding another signer, for example a Trezor/Ledger, making it default, and disabling the email/password signer.
For more info on signers, see Signers.